Molecular mechanics and electrostatic effects.

Continuum solvent models predict a quadratic charge dependence (linear response) of the free energy of a system of charged solutes. The relation between this prediction and the structure of the solvation shell around the solutes is discussed. Studies of the derivative of the free energy with respect to the charges for different reference states are shown to be a convenient way of testing the linear response assumption without resorting to the standard free energy perturbation method. We illustrate this with a system of two oppositely charged ions in aqueous solution, where nonlinearities are observed before the full charging process is completed. Since molecular mechanics (MM) simulations preserve the full nonlinearity of the problem, they are well suited to the investigation of the conditions under which linear response accurately reflects the behavior of the system. The error when using linear response theory to calculate the free energies of charging is estimated to be as large as 10-20%.